A contractor is considering the purchase of a new $$275,000$ grader, which has an estimated useful life of $8$ years. He believes that he can sell the used grader for $$50,000$ at the end of the $8$ years. Annual operating costs are estimated to be $$25,000$ per year. The annual interest rate is $6\%.$

$($a$)$ What is the number of time periods $($n$)$ you should use in solving this problem?

$($b$)$ What rate of interest $($i$),$ per period of time, should be use in solving this problem?

$($c$)$ Which time value factor should be used to find the annual cost of the purchase amount? $($Put your answer in terms of the shorthand potation.$)$

$($d$)$ What is the table value of the factor you identified in part $($c$)$ above?

$($e$)$ Which time value factor should be used to find the annual cost of the salvage amount? $($Put your answer in terms of the shorthand notation.$)$

$($f$)$ What is the table value of the factor you identified in part $($e$)$ above?

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